Research

In equilibrium, strong correlation between electrons yields various physical properties and quantum phases. By driving correlated systems out of equilibrium with external fields, one can expect even richer physics such as photo-induced phase transitions and observation of collective modes. Due to recent and rapid development of laser techniques, we can now excite and observe systems under various situations and new non-equilibrium phenomena are reported one after another. Important examples include possibility of photo-induced superconductors and topological insulators, observation of the Higgs mode in superconductors and high-harmonic generation in condensed matters. Nonequilibrium physics of correlated materials and strong laser field is now rapidly growing.

Motivated by these situations, I theoretically study nonequilibrium physics of strongly correlated systems and ordered phases. Our major motivations are to understand mechanism of various types of photo-induced phase transitions, to explore new types of nonequilibrium phenomena , and to establish measurement techniques using strong fields. We are also interested in developing numerical techniques and theoretical frameworks to study nonequilibrium physics.

High harmonic generation in strongly correlated systems

High-harmonic generation (HHG) is an intriguing nonlinear phenomenon indued by a strong electric field. It has been originally observed and studied in atomic and molecular gases, and is used in attosecond laser sources as well as spectroscopies. An observation of HHG in semiconductors expanded the scope of this field to condensed matters . The HHG in condensed matters is attracting interests since it may be used as new laser sources and/or as powerful tools to detect band information such as the Berry curvatures. Recently, further exploration of the HHG in condensed matters are carried out in various other systems than semiconductors.

Motivated by this situation, we have recently been theoretically studying the HHG in strongly correlated systems [1,2]. In contract to semiconductors, charge carriers are not normal fermions, which makes the HHG in strongly correlated systems nontrivial. There are many fundamental and important questions: What is the origin of the HHG in strongly correlated systems? How is it similar to or different from the HHG in semiconductors ? What information is included and whether we can use the HHG to measure some electronic structures? Using the dynamical-mean field theory and the infinite time-evolving block decimation for the Hubbard model, we answered to these questions [1,2]. We revealed that the origin of the HHG in the Mott insulator is the recombination of doublons (doubly occupied sites) and holons (no electron site). We show that the HHG feature qualitatively changes depending on the field strength due to the change of mobility of charge carriers, and discuss that the HHG directly reflects the dynamics of many body elemental excitations, which the single particle spectrum may miss. These results indicate that the HHG in Mott systems may be used as a spectroscopic tool for many body excitations. We also revealed the effects of spin dynamics on the HHG, which is a unique feature in strongly correlated systems. Besides the simple Hubbard system, we also studied spin systems [3] and multi-orbital Mott systems [4] and showed that characteristic excitations in these systems such as magnons and string states are reflected in their HHG structure.


When we started to investigate HHG in strongly correlated systems, there were no experimental reports. However, it has recently reported by Tanaka-group in Kyoto University (arXiv:2106.15478) that a strongly correlated system Ca2RuO4 shows peculiar HHG properties, which are anomalous compared to the HHG in normal semiconductors. We expect that there are plenty of new physics hidden in the HHG in strongly correlated systems.


  1. Yuta Murakami, Martin Eckstein and Philipp Werner “High-Harmonic Generation in Mott Insulators” Phys. Rev. Lett. 121, 057405 (2018).

  2. Yuta Murakami, Shintaro Takayoshi, Akihisa Koga, Philipp Werner “High-harmonic generation in one-dimensional Mott insulators” Phys. Rev. B 103, 035110 (2021).

  3. Shintaro Takayoshi, Yuta Murakami, Philipp Werner “High-harmonic generation in quantum spin systems” Phys. Rev. B 99, 184303 (2019), Editors’ suggestion.

  4. Markus Lysne, Yuta Murakami, Philipp Werner "Signatures of bosonic excitations in high-harmonic spectra of Mott insulators" Phys. Rev. B 101, 195139 (2020).

Emergence and control of nonequilibrium phases

[To be updated]

Controlling physical properties and inducing new phases using lasers are one of the major goal of nonequilibrium condensed matter physics. We have made extensive efforts in this directions and reported interesting examples and concepts. Please look up the following picked-up papers.
One of the lates work in this direction is Ref.[4], where we introduced a new theoretical framework to study nonequilibrium states using equilibrium methods.


  1. Yuta Murakami, Naoto Tsuji, Martin Eckstein, Philipp Werner “Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving” Phys. Rev. B 96, 045125 (2017), Editors’ suggestion.

  2. Philipp Werner, Yuta Murakami “Nonthermal excitonic condensation near a spin-state transition” Phys. Rev. B 102, 241103 (2020), Rapid communication.

  3. Yuta Murakami, Denis Golez, Martin Eckstein and Philipp Werner "Photo-induced Enhancement of Excitonic Order" Phys. Rev. Lett. 119, 247601 (2017).

  4. Yuta Murakami, Shintaro Takayoshi, Tatsuya Kaneko, Zhiyuan Sun, Denis Golež, Andrew J. Millis, Philipp Werner “Emergent nonequilibrium phases in the photo-doped one-dimensional Mott insulator” arXiv:2105.13560.

Collective modes in ordered phase

[To be updated]

We have been studied the nature of collective modes in ordered phases, in particular, superconductors [1,2] and excitonic insulators [3]. In candidate materials in excitonic insulators, observation of collective modes are crucial since the candidate phase of the excitonic insulator is alway accompanied by structural deformation. Through a collaboration with experimentalists, we recently reported an anomalous propagating mode in a candidate material, Ta2NiSe5, which may be a low lying phase mode [4].


  1. Yuta Murakami, Philipp Werner, Naoto Tsuji, and Hideo Aoki "Multiple amplitude modes in strongly coupled phonon-mediated superconductors"

Phys. Rev. B 93. 094509 (2016).

  1. Naoto Tsuji, Yuta Murakami, and Hideo Aoki "Nonlinear light–Higgs coupling in superconductors beyond BCS: Effects of the retarded phonon-mediated interaction" Phys. Rev. B 94. 224519 (2016).

  2. Yuta Murakami, Denis Golež, Tatsuya Kaneko, Akihisa Koga, Andrew J Millis, Philipp Werner “Collective modes in excitonic insulators: Effects of electron-phonon coupling and signatures in the optical response” Phys. Rev. B 101, 195118 (2020), Editors’ suggestion.

  3. Paolo Andrich, Hope M Bretscher, Yuta Murakami, Denis Golež, Benjamin Remez, Prachi Telang, Anupam Singh, Luminita Harnagea, Nigel R Cooper, Andrew J Millis, Philipp Werner, AK Sood, Akshay Rao “Imaging the coherent propagation of collective modes in the excitonic insulator candidate Ta2NiSe at room temperature”

Sci. Adv. 7 (28), eabd6147.

Development & assessment of theoretical methods

It is hard to treat many body problem even in equilibrium. Out of equilibrium, the treatment becomes even harder and theoretical methods are limited. Therefore, development of new theoretical techniques are very important in the study of nonequilibrium condensed matter physics. So far, we developed theoretical methods based on Green's function methods, in particular the nonequilibrium dynamical mean-field theory (DMFT). For example, in Refs [1,2], we developed methods to study transient dynamics and steady states in electron-phonon systems based on DMFT, which enable us to study the Higgs mode in strongly coupling superconductors and effects of phonon-excitations on nonequilibrium superconductors. In Ref. [3], we developed Floque DMFT using a strong coupling solver, which makes systematic study of driven Mott insulators possible. Furthermore, we recently made a direct comparison between the nonequilibrium DMFT and the cold atom experiment [4]. We studied the doublon creation rate under time-periodic external excitations to confirm the reliability of the theoretical method. We also made efforts to construct an open source library called NESSi (The Non-Equilibrium Systems Simulation package), which includes basic functions to develop nonequilibrium Green's function methods [5].


  1. Yuta Murakami, Philipp Werner, Naoto Tsuji, and Hideo Aoki "Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation" Phys. Rev. B 91, 045128 (2015).

  2. Yuta Murakami, Naoto Tsuji, Martin Eckstein and Philipp Werner "Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving" Phys. Rev. B 96, 045125 (2017), Editors' suggestion.

  3. Yuta Murakami and Philipp Werner “Nonequilibrium steady states of electric field driven Mott insulators” Phys. Rev. B 98, 075102 (2018).

  4. Kilian Sandholzer, Yuta Murakami, Frederik Görg, Joaquín Minguzzi, Michael Messer, Rémi Desbuquois, Martin Eckstein, Philipp Werner, Tilman Esslinger “Quantum simulation meets nonequilibrium DMFT: Analysis of a periodically driven, strongly correlated Fermi-Hubbard model” Phys. Rev. Lett. 123, 193602 (2019).

  5. Michael Schüler, Denis Golež, Yuta Murakami, Nikolaj Bittner, Andreas Herrmann, Hugo UR Strand, Philipp Werner, Martin Eckstein “NESSi: The Non-Equilibrium Systems Simulation package” Computer Physics Communications 257, 107484 (2020).